The underpayment penalty should not be increased however there is no reason to wait to file ... do so now then you can wait to pay up to 7/15. In the FILE tab choose to MAIL in the payment then either do so or pay the IRS directly online here : www.IRS.gov/payments
the underwithholding penalty is fixed . It is the late payment that accrues interest.
But the interest amount due was based on paying on April 14th. Can I wait until the June extension without having to recalculate the interest due?
It's not clear. From what I've read, there will be no additional interest. TurboTax is not capable of calculating the additional interest. So, if you wait to July 15 to pay, you'll just have to wait to see if the IRS bills you for the additional interest. Based on the current situation, that would be bad PR for the IRS and the administration